TY - BOOK ID - 8657140 TI - Explorations in Harmonic Analysis : With Applications to Complex Function Theory and the Heisenberg Group AU - Krantz, Steven G. AU - Lee, Lina PY - 2009 SN - 081764668X 9786613562104 1280384182 0817646698 PB - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, DB - UniCat KW - Electronic books. -- local. KW - Harmonic analysis. KW - Nilpotent Lie groups. KW - Harmonic analysis KW - Operations Research KW - Civil & Environmental Engineering KW - Engineering & Applied Sciences KW - Lie groups, Nilpotent KW - Analysis (Mathematics) KW - Functions, Potential KW - Potential functions KW - Mathematics. KW - Group theory. KW - Approximation theory. KW - Fourier analysis. KW - Functions of complex variables. KW - Mathematical models. KW - Abstract Harmonic Analysis. KW - Fourier Analysis. KW - Mathematical Modeling and Industrial Mathematics. KW - Approximations and Expansions. KW - Several Complex Variables and Analytic Spaces. KW - Group Theory and Generalizations. KW - Banach algebras KW - Calculus KW - Mathematical analysis KW - Mathematics KW - Bessel functions KW - Fourier series KW - Harmonic functions KW - Time-series analysis KW - Lie groups KW - Nilpotent groups KW - Differential equations, partial. KW - Groups, Theory of KW - Substitutions (Mathematics) KW - Algebra KW - Partial differential equations KW - Math KW - Science KW - Analysis, Fourier KW - Complex variables KW - Elliptic functions KW - Functions of real variables KW - Theory of approximation KW - Functional analysis KW - Functions KW - Polynomials KW - Chebyshev systems KW - Models, Mathematical KW - Simulation methods UR - https://www.unicat.be/uniCat?func=search&query=sysid:8657140 AB - This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis. Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and Poisson–Szegö integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous but well-paced exposition, this text provides all the necessary background in singular and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis. Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis. ER -